Problem: Let $p=3x+4$. Which equation is equivalent to $(3x+4)^2-36=15x+20$ in terms of $p$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $p^2-5p-56=0$ (Choice B) B $p^2-5p-36=0$ (Choice C) C $p^2+5p-36=0$ (Choice D) D $p^2+5p-56=0$
Solution: We are asked to rewrite the equation in terms of $p$, where ${p}={3x+4}$. In order to do this, we need to find all of the places where the expression ${3x+4}$ shows up in the equation, and then substitute ${p}$ wherever we see them! For instance, note that $15x+20=5({3x+4})$. This means that we can rewrite the equation as: $(3x+4)^2-36=15x+20$ $({3x+4})^2-36=5({3x+4})$ [What if I don't see this factorization?] Now we can substitute ${p}={3x+4}$ : $({p})^2-36=5({p})$ Finally, let's manipulate this expression so that it shares the same form as the answer choices: ${p}^2-5{p}-36=0$ In conclusion, $p^2-5p-36=0$ is equivalent to the given equation when $p=3x+4$.